John D. Corney disclosed a magnetic fluid-conditioning tool in his U.S. Pat. No. 5,178,757 by mounting magnets (15) on a flux-coupling cover member (33), with the flux-coupling cover member (33) mounted on each part (17a, 17b) of a core assembly (17). The two parts (17a, 17b) of the core assembly are then secured together by welding to form a flow passage (19) therebetween in the hollow tube (13). Each magnet (15) should be carefully secured on the flux-coupling cover member (33) and the two parts (17a, 17b) of the core assembly (17) should be welded together, thereby increasing the assembly complexity and production cost thereof.